反常输运现象中的分数阶扩散方程

 根据连续性方程,可以得到分形上的标准扩散方程。然而这个标准扩散方程并不能真正描述分形介质中的反常扩散,其根源在于分形介质中的扩散具有记忆效应,为了得到更普遍的扩散方程,通过讨论早期提出的扩散方程的缺陷,可以得到分数阶扩散方程,并且更具有普遍性。     

一种基于分形维数聚类的分形图像编码方法

对分形维数进行了探讨 ,提出了用分形维数对domainblocks进行聚类 ,从而达到了快速搜索编码的目的。实验结果表明 :与经典分形方法相比 ,在图像保真度基本接近的前提下 ,编码速度提高了 80倍左右     

单模激光系统中混沌吸引子的分维

对单模激光系统动力学行为的Ｌａｓｅｒ－Ｌｏｒｅｎｚ方程进行了线性稳定性分析,通过计算Ｌｙａｐｕｎｏｖ指数来确定该系统中混沌吸引子的分维。     

自调心伪双CCD光切360°三维轮廓测量系统

针对双 CCD三角测量系统的调心问题,提出一种利用单 CCD辅以可控机械回转臂实现光切 360°三维轮廓测量的新方案,给出了测量原理及系统结构,并详细介绍了映射函数法标定系统的原理及其具体实现.实物测量结果表明,该方法除具有双 CCD光切测量系统的全部优点外,测量系统可实现自动定心,后序数据融合简单,测量精度高,系统造价较低.     

Spin glass behavior upon diluting frustrated magnets and spin liquids: a Bethe-Peierls treatment

A Bethe-Peierls treatment to dilution in frustrated magnets and spin liquids is given. A spin glass phase is present at low temperatures and close to the percolation point as soon as frustration takes a finite value in the dilute magnet model; the spin glass phase is reentrant inside the ferromagnetic phase. An extension of the model is given, in which the spin glass/ferromagnet phase boundary is shown not to reenter inside the ferromagnetic phase asymptotically close to the tricritical point whereas it has a turning point at lower temperatures. We conjecture similar phase diagrams to exist in finite dimensional models not constraint by a Nishimori's line. We increase frustration to study the effect of dilution in a spin liquid state. This provides a “minimal” ordering by disorder from an Ising paramagnet to an Ising spin glass. Received 9 April 1999 and Received in final form 27 September 1999     

The fractional dimension identification method of critical bifurcated parameters of bearing-rotor system

ＩｎｔｒｏｄｕｃｔｉｏｎＢｉｆｕｒｃａｔｉｏｎａｎｄｆｒａｃｔａｌｔｈｅｏｒｙａｒｅｔｗｏｉｍｐｏｒｔａｎｔｂｒａｎｃｈｅｓｏｆｎｏｎｌｉｎｅａｒｓｃｉｅｎｃｅ.Ｔｈｅｂｉｆｕｒｃａｔｉｏｎｉｓ:ｆｏｒｃｏｎｔｉｎｕｏｕｓ＿ｔｉｍｅｄｙｎａｍｉｃａｌｓｙｓｔｅｍｘ=ｆ(ｘ,ｔ,α)ｏｒｄｉｓｃｒｅｔｅｄｙｎａｍｉｃａｌｓｙｓｔｅｍｘ｜→ｇ(ｘ,α)(ｗｈｅｒｅｇｉｓｍａｐｇ:Ｒｎ×Ｒ→Ｒｎ),ｗｈｅｎｔｈｅｐａｒａｍｅｔｅｒαｃｈａｎｇｅｓｃｏｎｔｉｎｕｏｕｓｌｙａｎｄｐａｓｓｅｓα0,ｔｈｅｔｏｐｏｌｏｇｉｃ…     

Anomalous diffusion in fractal porous medium

ＩｎｔｒｏｄｕｃｔｉｏｎＡｎｕｍｂｅｒｏｆｆｉｅｌｄｄａｔａｈａｖｅｓｈｏｗｎｔｈａｔｍａｎｙｋｉｎｄｓｏｆｐｏｒｏｕｓｍｅｄｉａｓｙｓｔｅｍｈａｖｅｄｉｆｆｅｒｅｎｔｋｉｎｄｓｏｆｈｅｔｅｒｏｇｅｎｅｏｕｓｓｔｒｕｃｔｕｒｅｉｎｄｉｆｆｅｒｅｎｔｓｃａｌｅ.Ｔｈｅｓｅｈｅｔｅｒｏｇｅｎｅｏｕｓｓｔｒｕｃｔｕｒｅａｓｓｏｃｉａｔｅｗｉｔｈｅａｃｈｏｔｈｅｒａｎｄｈａｖｅｓｏｍｅｋｉｎｄｓｏｆｓｅｌｆ＿ｓｉｍｉｌａｒｉｔｙａｎｄｗｅｃａｌｌｔｈｉｓｋｉｎｄｐｏｒｏｕｓｍｅｄｉａａｓｆｒａｃｔａｌｐ…     

Impact Dynamics in Milling of Thin-Walled Structures

The development of reliable high-speed spindles and motioncontrol systems has led to an increase in the industrial use ofhigh-speed milling. One of the primary applications of this newtechnology is the manufacture of thin-walled aluminum components foraircraft. The flexibility of the tools and workpieces, the high spindlefrequencies, and the inherent impact nonlinearities in the millingprocess can lead to complicated dynamic tool-workpieceinteractions. An experiment was constructed to study the vibrations ofa thin-walled part during milling. Time series, power spectra,autocorrelations, auto-bispectra, and phase portraits were examined.From this data, it is inferred that stiffness and damping nonlinearitiesdue to the intermittent cutting action have a pronounced effect on thedynamics of the workpiece. Delay space reconstructions and pointwisedimension calculations show that the associated motions arecharacterized by a fractal geometry. The auto-bispectra suggestquadratic phase coupling among the spectral peaks associated with thecutter frequency. A mechanics-based model with impact-nonlinearities wasdeveloped to explain the observed results. The predicted results agreewell with the experimental observations. The model predictions indicatethat aperiodic motions are possible over a large range ofcontrol-parameter values. These analytical and experimental results haveimplications for the prediction and control of vibrations in milling.     

An Event Dimension for Modeling Damping Due to Time-Varying Forcing Frequency

This article presents an original method for evaluating thedissipative effect in SDOF systems due to the transient phenomenongenerated by time-varying forcing frequencies. The main contributionlies in the use of an event dimension, as additional dimension, andEinstein's method for highlighting and proving the existence of adamping term in the equation of the motion. The variational problem ofthe metric of a pseudo-Riemannian space gives the geodesic equations andthe equation of the motion. The application is concerned with aspring-pendulum system and the associated experimental investigationpermits validating the method proposed. The influence of the variationof the forcing frequency is highlighted using two different load cases:it is shown that the damping depends on the forcing frequency variation.     

关于凝聚局部环的正则性

本文证明了极大理想m是有限生成的交换凝聚局部环（R,M）是正则的充分必要条件是m可以由一个正则R-序列生成,推广了文献[1]中相应的结论并给出了一个由正则凝聚局部环构造大量的非正则凝聚局部环的方法．